Abstract:
Most students learn about logarithms in intermediate algebra and elementary functions using exponential functions and the concept of an inverse function.

The early history of logarithms had some less obvious (from today's viewpoint) origins related to geometric and arithmetic rates of change and finding areas related to hyperbolas.

Professor Flashman will examine some of this early history of logarithms including

(I) Napier's 1616 original definition and tables of logarithms,

(II) the work of Gregoire de Saint-Vincent in 1647, and

(III) Newton's 1676 approach to estimating some values of natural (or hyperbolic) logarithms.

Part I 

John Napier

Napier's logarithms  (1616, 1619)

 (Text in html from the Netherlands).

A table (based on 100) that demonstrates the idea.

How would one use Napier's Tables:

Example: The rule of 3.
Suppose a/b = c/d.
Given any three of these values, find the fourth.

Napier's Theorem: If a/b=c/d then
NOG(a)- NOG(b) = NOG(c)-NOG(d)

Napier's logarithm tables.
 

Making Napier logarithm tables. (MS Excel)
 

If time permits (at the end):
How do Napier logarithms compare with modern logarithms?
 

Part II. Gregoire de St. Vincent and hyperbolic areas.